(245e) Expanding Resilient Lyapunov-Based Economic Model Predictive Control Concepts to a Distributed Control Framework

Distributed control is a technique with potential advantages in terms of computation time and tractability in controlling large-scale cyber physical systems. From a cybersecurity perspective, however, the increased number of information-passing connections relative to centralized control increases the opportunity for attackers to gain access to a component of a distributed system, which may impact process safety and/or profitability [2]. Specifically, false state measurements and other types of attacks have the potential to impact the performance of one or many controllers in the network. At the same time, distributed control offers more controllers with the potential capability to cross-check one another, ideally to pinpoint ones that cause problems on the network and remove them. To be able to analyze resilience of distributed controllers to attacks, it is desirable to utilize a distributed control framework that has strong closed-loop stability and feasibility guarantees in a centralized context. Lyapunov-based economic model predictive control (LEMPC) [5] is an optimization-based control technique that is able to guarantee closed-loop stability and recursive feasibility even in the presence of sufficiently small bounded disturbances. Already, several works have looked at how LEMPC relates to control system cybersecurity. For example, centralized LEMPC is explored with respect to guarantees which can be made in the presence of attacks for centralized control designs in [3] and [4]. Machine learning and data based methods related to cybersecurity have also been considered in conjunction with LEMPC [1]. However, despite a strong theoretical basis for distributed LEMPC [6, 7], integrating this framework with the detection policies for sensor measurement cyberattacks in [4] has not yet been explored, and further investigation of how the distributed framework might lend itself to means for isolating problematic controllers on the network with stability guarantees also must be performed.

Motivated by these considerations, this talk will extend three cyberattack detection strategies of [4] to a distributed control framework (both iterative and sequential LEMPC [6, 7]). The stability guarantees will be characterized, and in particular the challenges with diagnosing which of the distributed controllers is experiencing an attack if there is a discrepancy compared to what is expected (if, for example, the Lyapunov function should decrease in each of a set of sequential distributed controllers, and is found not to in one in the sequence). We also discuss a methodology, inspired by [8], for removing a controller that might have been attacked (e.g., re-coded) from a network (as in [8], it may be possible to operate the process with a reduced set of control actions if returned to a region around the steady state), and then seeking to introduce a level of randomization in the manner in which control actions are subsequently computed between the isolated controller and the remaining controllers to attempt to make it harder for an attacker to remove specific controllers in an attempt to generate a characterizable behavior with the network.

[1] Chen, Scarlett, Zhe Wu, and Panagiotis D. Christofides. "Cyber-attack detection and resilient operation of nonlinear processes under economic model predictive control." Computers & Chemical Engineering 136 (2020): 106806.

[2] Chen, Scarlett, Zhe Wu, and Panagiotis D. Christofides. "Cyber-security of centralized, decentralized, and distributed control-detector architectures for nonlinear processes." Chemical Engineering Research and Design 165 (2021): 25-39.

[3] Durand, Helen. "A nonlinear systems framework for cyberattack prevention for chemical process control systems." Mathematics 6.9 (2018): 169.

[4] Oyama, Henrique, and Helen Durand. "Integrated cyberattack detection and resilient control strategies using Lyapunov‐based economic model predictive control." AIChE Journal 66.12 (2020): e17084.

[5] Heidarinejad, Mohsen, Jinfeng Liu, and Panagiotis D. Christofides. "Economic model predictive control of nonlinear process systems using Lyapunov techniques." AIChE Journal 58.3 (2012): 855-870.

[6] Liu, Jinfeng, Xianzhong Chen, David Muñoz de la Peña, and Panagiotis D. Christofides. "Sequential and iterative architectures for distributed model predictive control of nonlinear process systems." AIChE Journal 56, no. 8 (2010): 2137-2149.

[7] Albalawi, Fahad, Helen Durand, and Panagiotis D. Christofides. "Distributed economic model predictive control for operational safety of nonlinear processes." AIChE Journal 63.8 (2017): 3404-3418.

[8] Lao, Liangfeng, Matthew Ellis, and Panagiotis D. Christofides. "Smart manufacturing: Handling preventive actuator maintenance and economics using model predictive control." AIChE Journal 60.6 (2014): 2179-2196.